Now we compare the detailed electronic structure differences of the two ions from SCAN and PBE0-TS.
First, as shown in Figs. REF (a), (b), and (c),
a larger distance between oxygen and proton (the length of O-H covalent bond)
suggests that oxygen binds more loosely with the proton,
and SCAN is known to strengthen the covalent bonds as compared to PBE [1]};
here we find PBE0-TS yields protons that locate closer to the oxygen atom,
implying a stronger covalent bond as compared to SCAN.
Besides, for the pure water described by the SCAN functional,
both lone pairs and bonding pairs of ambient liquid water molecules shown in Fig. REF (b)
shift closer to the oxygen atom.
This indicates that SCAN provides a less negatively charged environment
on the oxygen site and a more positively charged environment on the proton side for pure liquid water.
In other words, the oxygen and proton sites of water molecules respectively
become more hydrophobic and more hydrophilic in the SCAN trajectory than in the PBE0-TS counterpart.
The two competing effects lead to a more pronounced first peak of radial distribution functions as observed in Figs. REF (c) and (d), which implies that SCAN provides a more strengthened HB at a short-range scale when compared to PBE0-TS.
